GH Bladed TheoryManual

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(1)GH Bladed Theory Manual Document No Classification Issue no. Date. 282/BR/009 Commercial in Confidence 11 July 2003. Author: E A Bossanyi Checked by: D C Quarton Approved by: D C Quarton.

(2) DISCLAIMER Acceptance of this document by the client is on the basis that Garrad Hassan and Partners Limited are not in any way to be held responsible for the application or use made of the findings of the results from the analysis and that such responsibility remains with the client.. Key To Document Classification Strictly Confidential. :. Recipients only. Private and Confidential. :. For disclosure to individuals directly concerned within the recipient’s organisation. Commercial in Confidence. :. Not to be disclosed outside the recipient’s organisation. GHP only. :. Not to be disclosed to non GHP staff. Client’s Discretion. :. Distribution at the discretion of the client subject to contractual agreement. Published. :. Available to the general public. © 2003 Garrad Hassan and Partners Limited.

(3) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. CONTENTS. 1.. Introduction 1.1 1.2 1.3 1.4 1.5. 2.. 1. Purpose Theoretical background Support Documentation Acknowledgements. 1 2 3 3 3. AERODYNAMICS. 4. 2.1. Combined blade element and momentum theory 2.1.1 Actuator disk model 2.1.2 Wake rotation 2.1.3 Blade element theory 2.1.4 Tip and hub loss models 2.2 Wake models 2.2.1 Equilibrium wake 2.2.2 Frozen wake 2.2.3 Dynamic wake 2.3 Steady stall 2.4 Dynamic stall. 3.. STRUCTURAL DYNAMICS. 13. 3.1. Modal analysis 3.1.1 Rotor modes 3.1.2 Tower modes 3.2 Equations of motion 3.2.1 Degrees of freedom 3.2.2 Formulation of equations of motion 3.2.3 Solution of the equations of motion 3.3 Calculation of structural loads. 4. 4.1. 4.2. 4.3 4.4 4.5. 5. 5.1 5.2. 4 4 5 6 8 9 9 9 9 11 11 13 14 15 16 16 16 17 18. POWER TRAIN DYNAMICS. 19. Drive train models 4.1.1 Locked speed model 4.1.2 Rigid shaft model 4.1.3 Flexible shaft model Generator models 4.2.1 Fixed speed induction generator 4.2.2 Fixed speed induction generator: electrical model 4.2.3 Variable speed generator 4.2.4 Variable slip generator Drive train mounting Energy losses The electrical network. 19 19 19 19 20 20 21 22 23 24 24 25. CLOSED LOOP CONTROL. 27. Introduction The fixed speed pitch regulated controller. -i-. 27 27.

(4) Garrad Hassan and Partners Ltd. Document: 282/BR/009. 5.2.1 Steady state parameters 5.2.2 Dynamic parameters 5.3 The variable speed stall regulated controller 5.3.1 Steady state parameters 5.3.2 Dynamic parameters 5.4 The variable speed pitch regulated controller 5.4.1 Steady state parameters 5.4.2 Dynamic parameters 5.5 Transducer models 5.6 Modelling the pitch actuator 5.7 The PI control algorithm 5.7.1 Gain scheduling 5.8 Control mode changes 5.9 Client-specific controllers 5.10 Signal noise and discretisation. 6.. SUPERVISORY CONTROL. ISSUE:011. FINAL. 28 28 28 28 30 31 31 32 33 33 36 37 38 38 39. 40. 6.1 6.2 6.3 6.4 6.5 6.6. Start-up Normal stops Emergency stops Brake dynamics Idling and parked simulations Yaw control 6.6.1 Active yaw 6.6.2 Yaw dynamics 6.7 Teeter restraint. 40 41 41 42 42 42 42 43 44. MODELLING THE WIND. 45. Wind shear 7.1.1 Exponential model 7.1.2 Logarithmic model Tower shadow 7.2.1 Potential flow model 7.2.2 Empirical model 7.2.3 Combined model Upwind turbine wake 7.3.1 Eddy viscosity model of the upwind turbine wake 7.3.2 Turbulence in the wake Time varying wind 7.4.1 Single point time history 7.4.2 3D turbulent wind 7.4.3 IEC transients Three dimensional turbulence model 7.5.1 The basic von Karman model 7.5.2 The improved von Karman model 7.5.3 The Kaimal model 7.5.4 Compatibility with IEC 1400-1 7.5.5 Using 3d turbulent wind fields in simulations. 46 46 46 46 46 47 47 47 48 50 51 51 51 52 53 53 55 59 59 59. MODELLING WAVES AND CURRENTS. 61. 7. 7.1 7.2. 7.3 7.4. 7.5. 8. 8.1 8.2. Tower and Foundation Model Wave Spectra. 61 62 - ii -.

(5) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. 8.2.1 JONSWAP / Pierson-Moskowitz Spectrum 8.2.2 User-defined Spectrum 8.3 Upper Frequency Limit 8.4 Wave Particle Kinematics 8.5 Wheeler Stretching 8.6 Simulation of Irregular Waves 8.7 Simulation of Regular Waves 8.8 Current Velocities 8.8.1 Near-Surface Current 8.8.2 Sub-Surface Current 8.8.3 Near-Shore Current 8.9 Total Velocities and Accelerations 8.10 Applied Forces 8.10.1 Relative Motion Form of Morison’s Equation 8.10.2 Longitudinal Pressure Forces on Cylindrical Elements. 9.. POST-PROCESSING. 62 62 63 63 64 64 66 67 68 68 68 69 69 69 69. 71. 9.1 9.2 9.3 9.4 9.5 9.6. Basic statistics Fourier harmonics, and periodic and stochastic components Extreme prediction Spectral analysis Probability, peak and level crossing analysis Rainflow cycle counting and fatigue analysis 9.6.1 Rainflow cycle counting 9.6.2 Fatigue analysis 9.7 Annual energy yield 9.8 Ultimate loads 9.9 Flicker. 10.. FINAL. References. 71 71 72 75 75 76 76 77 78 79 79. 80. - iii -.

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(7) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 1. INTRODUCTION. 1.1 Purpose GH Bladed is an integrated software package for wind turbine performance and loading calculations. It is intended for the following applications: • Preliminary wind turbine design • Detailed design and component specification • Certification of wind turbines With its sophisticated graphical user interface, it allows the user to carry out the following tasks in a straightforward way: • Specification of all wind turbine parameters, wind inputs and load cases. • Rapid calculation of steady-state performance characteristics, including: Aerodynamic information Performance coefficients Power curves Steady operating loads Steady parked loads • Dynamic simulations covering the following cases: Normal running Start-up Normal and emergency shut-downs Idling Parked Dynamic power curve • Post-processing of results to obtain: Basic statistics Periodic component analysis Probability density, peak value and level crossing analysis Spectral analysis Cross-spectrum, coherence and transfer function analysis Rainflow cycle counting and fatigue analysis Combinations of variables Annual energy yield Ultimate loads (identification of worst cases) Flicker severity • Presentation: results may be presented graphically and can be combined into a word processor compatible report.. 1 of 82.

(8) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 1.2 Theoretical background The Garrad Hassan approach to the calculation of wind turbine performance and loading has been developed over many years. The main aim of this development has been to produce reliable tools for use in the design and certification of wind turbines. The models and theoretical methods incorporated in GH Bladed have been extensively validated against monitored data from a wide range of turbines of many different sizes and configurations, including: • • • • • • • • • • • • • • • • • • • • • • • • • • • •. WEG MS-1, UK, 1991 Howden HWP300 and HWP330, USA, 1993 ECN 25m HAT, Netherlands, 1993 Newinco 500kW, Netherlands, 1993 Nordex 26m, Denmark, 1993 Nibe A, Denmark, 1993 Holec WPS30, Netherlands, 1993 Riva Calzoni M30, Italy, 1993 Nordtank 300kW, Denmark, 1994 WindMaster 750kW, Netherlands, 1994 Tjaereborg 2MW, Denmark, 1994 Zond Z-40, USA, 1994 Nordtank 500kW, UK, 1995 Vestas V27, Greece, 1995 Danwin 200kW, Sweden, 1995 Carter 300kW, UK, 1995 NedWind 50, 1MW, Netherlands, 1996 DESA, 300kW, Spain 1997 NTK 600, UK, 1998 West Medit, Italy, 1998 Nordex 1.3 MW, Germany, 1999 The Wind Turbine Company 350 kW, USA, 2000 Windtec 1.3 MW, Austria, 2000 WEG MS-4, 400 kW, UK, 2000 EHN 1.3 MW, Spain, 2001 Vestas 2MW, UK, 2001 Lagerwey 750 Netherlands, 2001 Vergnet 200, France 2001. This document describes the theoretical background to the various models and numerical methods incorporated in GH Bladed.. 2 of 82.

(9) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 1.3 Support GH Bladed is supplied with a one-year maintenance and support agreement, which can be renewed for further periods. This support includes a ‘hot-line’ help service by telephone, fax or e-mail: Telephone: Fax: E-mail. +44 (0)117 972 9900 +44 (0)117 972 9901 bladed@bristol.garradhassan.co.uk. 1.4 Documentation In addition to this Theory Manual, there is also a GH Bladed User Manual which explains how the code can be used.. 1.5 Acknowledgements GH Bladed was developed with assistance from the Commission of the European Communities under the JOULE II programme, project no. JOU2-CT92-0198.. 3 of 82.

(10) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 2. AERODYNAMICS The modelling of rotor aerodynamics provided by Bladed is based on the well established treatment of combined blade element and momentum theory [2.1]. Two major extensions of this theory are provided as options in the code to deal with the unsteady nature of the aerodynamics. The first of these extensions allows a treatment of the dynamics of the wake and the second provides a representation of dynamic stall through the use of a stall hysteresis model. The theoretical background to the various aspects of the treatment of rotor aerodynamics provided by Bladed is given in the following sections.. 2.1 Combined blade element and momentum theory At the core of the aerodynamic model provided by Bladed is combined blade element and momentum theory. The features of this treatment of rotor aerodynamics are described below. 2.1.1 Actuator disk model To aid the understanding of combined blade element and momentum theory it is useful initially to consider the rotor as an “actuator disk”. Although this model is very simple, it does provide valuable insight into the aerodynamics of the rotor. Wind turbines extract energy from the wind by producing a step change in static pressure across the rotor-swept surface. As the air approaches the rotor it slows down gradually, resulting in an increase in static pressure. The reduction in static pressure across the rotor disk results in the air behind it being at sub atmospheric pressure. As the air proceeds downstream the pressure climbs back to the atmospheric value resulting in a further slowing down of the wind. There is therefore a reduction in the kinetic energy in the wind, some of which is converted into useful energy by the turbine. In the actuator disk model of the process described above, the wind velocity at the rotor disk Ud is related to the upstream wind velocity Uo as follows: U d = ( 1 a )U o. The reduced wind velocity at the rotor disk is clearly determined by the magnitude of a, the axial flow induction factor or inflow factor. By applying Bernoulli’s equation and assuming the flow to be uniform and incompressible, it can be shown that the power P extracted by the rotor is given by : P = 2 AU o3a( 1 a )3. where. is the air density and A the area of the rotor disk.. The thrust T acting on the rotor disk can similarly be derived to give:. 4 of 82.

(11) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. T = 2 AU o2 a( 1 a ). The dimensionless power and thrust coefficients, CP and CT are respectively: CP = P / ( 1 2 AU o3 ) = 4a( 1 a )2. and: CT = T / ( 1 2 AU o2 ) = 4a( 1 a ). The maximum value of the power coefficient CP occurs when a is 1 /3 and is equal to 16/27 which is known as the Betz limit. The thrust coefficient CT has a maximum value of 1 when a is 1 /2. 2.1.2 Wake rotation The actuator disk concept used above allows an estimate of the energy extracted from the wind without considering that the power absorbed by the rotor is the product of torque Q and angular velocity of the rotor. The torque developed by the rotor must impart an equal and opposite rate of change of angular momentum to the wind and therefore induces a tangential velocity to the flow. The change in tangential velocity is expressed in terms of a tangential flow induction factor a’. Upstream of the rotor disk the tangential velocity is zero, at the disk the tangential velocity at radius r on the rotor is ra’ and far downstream the tangential velocity is 2 ra’. Because it is produced in reaction to the torque, the tangential velocity is opposed to the motion of the blades. The torque generated by the rotor is equal to the rate of change of angular momentum and can be derived as: Q=. R 4 (1 a )a ,U o. 5 of 82.

(12) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 2.1.3 Blade element theory Combined blade element and momentum theory is an extension of the actuator disk theory described above. The rotor blades are divided into a number of blade elements and the theory outlined above used not for the rotor disk as a whole but for a series of annuli swept out by each blade element and where each annulus is assumed to act in the same way as an independent actuator disk. At each radial position the rate of change of axial and angular momentum are equated with the thrust and torque produced by each blade element. The thrust dT developed by a blade element of length dr located at a radius r is given by: dT = 1 2 W 2 ( CL cos + CD sin )cdr. where W is the magnitude of the apparent wind speed vector at the blade element, is known as the inflow angle and defines the direction of the apparent wind speed vector relative to the plane of rotation of the blade, c is the chord of the blade element and CL and CD are the lift and drag coefficients respectively. The lift and drag coefficients are defined for an aerofoil by: CL = L / ( 1 2 V 2 S ). and CD = D / ( 1 2 V 2 S ). where L and D are the lift and drag forces, S is the planform area of the aerofoil and V is the wind velocity relative to the aerofoil. The torque dQ developed by a blade element of length dr located at a radius r is given by: dQ = 1 2 W 2 r( CL sin. CD cos )cdr. In order to solve for the axial and tangential flow induction factors appropriate to the radial position of a particular blade element, the thrust and torque developed by the element are equated to the rate of change of axial and angular momentum through the annulus swept out by the element. Using expressions for the axial and angular momentum similar to those derived for the actuator disk in Sections 2.1.1 and 2.1.2 above, the annular induction factors may be expressed as follows: a = g1 / ( 1 + g1 ). and a , = g2 / ( 1 g 2 ). where 6 of 82.

(13) Garrad Hassan and Partners Ltd. Document: 282/BR/009. g1 =. Bc ( CL cos + CD sin ) H 2 r 4 F sin 2. g2 =. Bc ( CL sin CD cos ) 2 r 4 F sin cos. ISSUE:011. FINAL. and. Here B is the number of blades and F is a factor to take account of tip and hub losses, refer Section 2.1.4. The parameter H is defined as follows: for a. 0.3539, H = 10 .. for a > 0.3539, H =. 4a (1 a ) (0.6 + 0.61a + 0.79a 2 ). In the situation where the axial induction factor a is greater than 0.5, the rotor is heavily loaded and operating in what is referred to as the “turbulent wake state”. Under these conditions the actuator disk theory presented in Section 2.1.1 is no longer valid and the expression derived for the thrust coefficient: CT = 4a( 1 a ). must be replaced by the empirical expression: CT = 0.6 + 0.61a + 0.79a 2. The implementation of blade element theory in Bladed is based on a transition to the empirical model for values of a greater than 0.3539 rather than 0.5. This strategy results in a smoother transition between the models of the two flow states. The equations presented above for a and a’ can only be solved iteratively. The procedure involves making an initial estimate of a and a’, calculating the parameters g1 and g2 as functions of a and a’, and then using the equations above to update the values of a and a’. This procedure continues until a and a’ have converged on a solution. In Bladed convergence is assumed to have occurred when: ak. ak. 1. tol. a'k. a'k. 1. tol. and. where tol is the value of aerodynamic tolerance specified by the user.. 7 of 82.

(14) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 2.1.4 Tip and hub loss models The wake of the wind turbine rotor is made up of helical sheets of vorticity trailed from each rotor blade. As a result the induced velocities at a fixed point on the rotor disk are not constant with time, but fluctuate between the passage of each blade. The greater the pitch of the helical sheets and the fewer the number of blades, the greater the amplitude of the variation of induced velocities. The overall effect is to reduce the net momentum change and so reduce the net power extracted. If the induction factor a is defined as being the value which applies at the instant a blade passes a given point on the disk, then the average induction factor at that point, over the course of one revolution will be aFt,, where Ft is a factor which is less than unity. The circulation at the blade tips is reduced to zero by the wake vorticity in the same manner as at the tips of an aircraft wing. At the tips, therefore the factor Ft becomes zero. Because of the analogy with the aircraft wing , where losses are caused by the vortices trailing from the tips, Ft is known as the tip loss factor. Prandtl [2.2] put forward a method to deal with this effect in propeller theory. Reasoning that, in the far wake, the helical vortex sheets could be replaced by solid disks, set at the same pitch as the normal spacing between successive turns of the sheets, moving downstream with the speed of the wake. The flow velocity outside of the wake is the free stream value and so is faster than that of the disks. At the edges of the disks the fast moving free stream flow weaves in and out between them and in doing so causes the mean axial velocity between the disks to be higher than that of the disks themselves, thus simulating the reduction in the change of momentum. The factor Ft can be expressed in closed solution form: Ft = 2 arccos[exp(. s )] d. where s is the distance of the radial station from the tip of the rotor blade and d is the distance between successive helical sheets. A similar loss takes place at the blade root where, as at the tip, the bound circulation must fall to zero and therefore a vortex must be trailed into the wake, A separate hub loss factor Fh is therefore calculated and the effective total loss factor at any station on the blade is then the product of the two: F = Ft Fh. The combined tip and hub loss factor is incorporated in the equations of blade element theory as indicated in Section 2.1.3 above.. 8 of 82.

(15) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 2.2 Wake models 2.2.1 Equilibrium wake The use of blade element theory for time domain dynamic simulations of wind turbine behaviour has traditionally been based on the assumption that the wake reacts instantaneously to changes in blade loading. This treatment, known as an equilibrium wake model, involves a re-calculation of the axial and tangential induction factors at each element of each rotor blade, and at each time step of a dynamic simulation. Based on this treatment the induced velocities along each blade are computed as instantaneous solutions to the particular flow conditions and loading experienced by each element of each blade. Clearly in this interpretation of blade element theory the axial and tangential induced velocities at a particular blade element vary with time and are not constant within the annulus swept out by the element. The equilibrium wake treatment of blade element theory is the most computationally demanding of the three treatments described here. 2.2.2 Frozen wake In the frozen wake model, the axial and tangential induced velocities are computed using blade element theory for a uniform wind field at the mean hub height wind speed of the simulated wind conditions. The induced velocities, computed according to the mean, uniform flow conditions, are then assumed to be fixed, or “frozen” in time. The induced velocities vary from one element to the next along the blade but are constant within the annulus swept out by the element. As a consequence each blade experiences the same radial distribution of induced flow.. It is important to note that it is the axial and tangential induced velocities aUo and a’r not the induction factors a and a’ which are frozen in time.. and. 2.2.3 Dynamic wake As described above, the equilibrium wake model assumes that the wake and therefore the induced velocity flow field react instantaneously to changes in blade loading. On the other hand, the frozen wake model assumes that induced flow field is completely independent of changes in incident wind conditions and blade loading. In reality neither of these treatments is strictly correct. Changes in blade loading change the vorticity that is trailed into the rotor wake and the full effect of these changes takes a finite time to change the induced flow field. The dynamics associated with this process is commonly referred to as “dynamic inflow”. The study of dynamic inflow was initiated nearly 40 years ago in the context of helicopter aerodynamics. In brief, the theory provides a means of describing the dynamic dependence of the induced flow field at the rotor upon the loading that it experiences. The dynamic inflow model used within Bladed is based on the work of Pitt and Peters [2.3] which has received substantial validation in the helicopter field, see for example Gaonkar et al [2.4]. The Pitt and Peters model was originally developed for an actuator disk with assumptions made concerning the distribution of inflow across the disc. In Bladed the model is applied at blade element or actuator annuli level since this avoids any assumptions about the distribution of inflow across the disc. 9 of 82.

(16) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. For a blade element, bounded by radii R1 and R2 , and subject to uniform axial flow at a wind speed Uo, the elemental thrust, dT, can be expressed as: dT = 2U o am + U o m A a&. where m is the mass flow through the annulus, mA is the apparent mass acted upon by the annulus and a is the axial induction factor. The mass flow through the annular element is given by: m = U o (1 a )dA. where dA is the cross-sectional area of the annulus. For a disc of radius R the apparent mass upon which it acts is given approximately by potential theory, Tuckerman, [2.5]: mA = 8. 3. R3. Therefore the thrust coefficient associated with the annulus can be derived to give: C T = 4a (1 a ) +. 16 (R 32 3 U o (R 22. R 13 ) R 12 ). a&. This differential equation can therefore be used to replace the blade element and momentum theory equation for the calculation of axial inflow. The equation is integrated at each time step to give time dependent values of inflow for each blade element on each blade. The tangential inflow is obtained in the usual manner and so depends on the time dependent axial value. It is evident that the equation introduces a time lag into the calculation of inflow which is dependent on the radial station. It is probable that the values of time lag for each blade element calculated in this manner will under-estimate somewhat the effects of dynamic inflow, as each element is treated independently with no consideration of the three dimensional nature of the wake or the possibly dominant effect of the tip vortex. The treatment is, however, consistent with blade element theory and provides a simple, computationally inexpensive and reasonably reliable method of modelling the dynamics of the rotor wake and induced velocity flow field.. 10 of 82.

(17) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 2.3 Steady stall The representation and to some extent the general understanding of aerodynamic stall on a rotating wind turbine blade remain rather poor. This is a rather extraordinary situation in view of the importance of stall regulation to the industry. Stall delay on the inboard sections of rotor blades, due to the three dimensionality of the incident flow field, has been widely confirmed by measurements at both model and full scale. A number of semi-empirical models [2.6, 2.7] have been developed for correcting two dimensional aerofoil data to account for stall delay. Although such models are used for the design analysis of stall regulated rotors, their general validity for use with a wide range of aerofoil sections and rotor configurations remains, at present, rather poor. As a consequence Bladed does not incorporate models for the modification of aerofoil data to deal with stall delay, but the user is clearly able to apply whatever correction of the aerofoil data he believes is appropriate prior to its input to the code.. 2.4 Dynamic stall Stall and its consequences are fundamentally important to the design and operation of most aerodynamic devices. Most conventional aeronautical applications avoid stall by operating well below the static stall angle of any aerofoils used. Helicopters and stall regulated wind turbines do however operate in regimes where at least part of their rotor blades are in stall. Indeed stall regulated wind turbines rely on the stalling behaviour of aerofoils to limit maximum power output from the rotor in high winds. A certain degree of unsteadiness always accompanies the turbulent flow over an aerofoil at high angles of attack. The stall of a lifting surface undergoing unsteady motion is more complex than static stall. On an oscillating aerofoil, where the incidence is increasing rapidly, the onset of the stall can be delayed to an incidence considerably in excess of the static stall angle. When dynamic stall does occur, however, it is usually more severe than static stall. The attendant aerodynamic forces and moments exhibit large hysteresis with respect to the instantaneous angle of attack, especially if the oscillation is about a mean angle close to the static stall angle. This represents an important contrast to the quasi-steady case, for which the flow field adjusts immediately, and uniquely, to each change in incidence. Many methods of predicting the dynamic stall of aerofoil sections have been developed, principally for use in the helicopter industry. The model adopted for inclusion of unsteady behaviour of aerofoils is that due to Beddoes [2.8]. The Beddoes model was developed for use in helicopter rotor performance calculations and has been formulated over a number of years with particular reference to dynamic wind tunnel testing of aerofoil sections used on helicopter rotors. It has been used successfully by Harris [2.9] and Galbraith et al [2.10] in the prediction of the behaviour of vertical axis wind turbines.. 11 of 82.

(18) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. The model used within Bladed is a development of the Beddoes model which has been validated against measurements from several stall regulated wind turbines. The model utilises the following elements of the method described in [2.8] to calculate the unsteady lift coefficient • The indicial response functions for modelling of attached flow • The time lagged Kirchoff formulation for the modelling of trailing edge separation and vortex lift The use of the model of leading edge separation has been found to be inappropriate for use on horizontal axis wind turbines where the aerofoil characteristics are dominated by progressive trailing edge stall. The time lag in the development of trailing edge separation is a user defined parameter within the model implemented in Bladed. This time lag encompasses the delay in the response of the pressure distribution and boundary layer to the time varying angle of attack. The magnitude of the time lag is directly related to the level of hysteresis in the lift coefficient. The drag and pitching moment coefficients are calculated using the quasi-steady input data along with the effective unsteady angle of attack determined during the calculation of the lift coefficient.. 12 of 82.

(19) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 3. STRUCTURAL DYNAMICS In the early days of the industry, wind turbine design was undertaken on the basis of quasistatic aerodynamic calculations with the effects of structural dynamics either ignored completely or included through the use of estimated dynamic magnification factors. From the late 1970’s research workers began to consider more reliable methods of dynamic analysis and two basic approaches were considered: finite element representations and modal analysis. The traditional use of standard, commercial finite element analysis codes for dealing with problems of structural dynamics is problematic in the case of wind turbines. This is because of the gross movement of one component of the structure, the rotor, with respect to another, the tower. Standard finite element packages are only used to consider structures in which motion occurs about a mean undisplaced position and for this reason the finite element models of wind turbines which have been developed have been specially constructed to deal with the problem. The form of wind turbine dynamic modelling most commonly used as the basis of design calculations is that involving a modal representation. This approach, borrowed from the helicopter industry, has the major advantage that it offers a reliable representation of the dynamics of a wind turbine with relatively few degrees of freedom. The number and type of modal degrees of freedom used to represent the dynamics of a particular wind turbine will clearly depend on the configuration and structural properties of the machine. At present, largely because of the very extensive computer processing requirements associated with the use of finite element models, the state of the art in the context of wind turbine dynamic modelling for design analysis is based squarely on the use of limited degree of freedom modal models. The representation of wind turbine structural dynamics within Bladed is based on a modal model.. 3.1 Modal analysis Because of the rotation of the blades of a wind turbine relative to the tower support structure, the equations of motion which describe its dynamics contain terms with periodic coefficients. This periodicity means that the computation of the modal properties of an operating wind turbine as a complete structural entity is not possible using the standard eigen-analysis offered by commercial finite element codes. One solution to this problem is to make use of Floquet analysis to determine the modal properties of the periodic system. However, the mode shapes obtained by such calculations are complex and not directly useful for a forced response analysis. An alternative solution is based on the use of “component mode synthesis”. Here the modal properties of the rotating and non-rotating components of the wind turbine are computed independently. The component modes are then coupled by an appropriate formulation of the equations of motion of the wind turbine in the forced response analysis. This approach has been adopted for Bladed.. 13 of 82.

(20) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 3.1.1 Rotor modes The vibration of the tapered and twisted blades of a wind turbine rotor is a complex phenomenon. A classical method of representing the vibration is by means of the orthogonal, uncoupled “normal” modes of the structure. Each mode is defined in terms of the following parameters: • Modal frequency,. i. • Modal damping coefficient, • Mode shape,. i. i. (r ). where the subscript i indicates properties related to the ith mode. The modal frequencies and mode shapes of the rotor are calculated based on the following information: The mass distribution along the blade. The mass distribution is defined as the local mass density (kg/m) at each radial station in addition to the magnitude and location of any discrete, lumped masses. The bending stiffnesses along the blade. The bending stiffnesses are defined in local flapwise and edgewise directions at each radial station. The twist angle distribution along the blade. The mode shapes are computed in the rotor in-plane and out-of-plane directions and hence the flapwise and edgewise stiffnesses at each radial station are resolved through the local twist angle. The blade pitch and setting angles. The mode shapes are computed in the rotor in-plane and out-of-plane directions and hence the flapwise and edgewise stiffnesses at each radial station are resolved through the blade pitch and setting angles. The user of Bladed may select a series of different pitch angles for which the modal analysis is carried out. During subsequent dynamic simulations, the modal frequencies appropriate to the instantaneous blade pitch angle are therefore obtained by linear interpolation of the results of the modal analyses. The presence or otherwise of a hub teeter hinge for a two bladed rotor. For a two-bladed rotor the hub can be rigid or teetered. The presence of a teeter hinge will introduce asymmetric rotor modes involving out-of-plane rotation of the rotor about the teeter hinge. The presence or otherwise of a flap hinge for a one-bladed rotor. For a one-bladed rotor the hub can be rigid or have a flap hinge. The presence of a flap hinge will introduce rotor modes involving out-of-plane rotation of the rotor about the teeter hinge. The counter-weight mass and moment of inertia about the flap hinge for a one-bladed rotor. Whether the hub can rotate. 14 of 82.

(21) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. Rotation of the hub will affect the frequencies and mode shapes of the in-plane rotor modes. With the shaft brake engaged and the rotor locked in position, the in-plane modes will include both symmetric and asymmetric cantilever-type modes. With the rotor free to rotate, the cantilever-type asymmetric modes will be replaced by asymmetric modes involving rotation about the rotor shaft. The rotational speed of the rotor. The frequencies and mode shapes of both in-plane and out-of-plane modes will be dependent on the rotational speed of the rotor. This dependence is explained by the additional bending stiffness developed because of centrifugal loads acting on the deflected rotor blades. The user of Bladed may select different rotational speeds for which the modal analysis is carried out. During subsequent dynamic simulations, the modal frequencies appropriate to the instantaneous rotational speed are therefore obtained by quadratic interpolation of the results of the modal analyses. The frequencies and mode shapes of the rotor modes are computed from the eigen-values and eigen-vectors of a finite element representation of the rotor structure. The finite element model of the rotor is based on the use of two-dimensional beam elements to describe the mass and stiffness properties of the rotor blades. The outputs from the modal analysis of the rotor are the modal frequencies and mode shapes defined in the rotor in-plane and out-of-plane directions. The modal damping coefficients are an input defined by the user and may be used to represent structural damping. 3.1.2 Tower modes The representation of the bending dynamics of the tower is based on the modal degrees of freedom in the fore-aft and side-side directions of motion. As for the rotor, the tower modes are defined in terms of their modal frequency, modal damping and mode shape. The modal frequencies and mode shapes of the tower are calculated based on the following information: The mass distribution along the tower. The mass distribution is defined as the local mass density (kg/m) at each tower station height in addition to the magnitude and location of any discrete, lumped masses. The bending stiffness along the tower. The tower is assumed to be axisymmetric with the bending stiffness therefore independent of bending direction. The mass, inertia and stiffness properties of the tower foundation. The influence of the foundation mass and stiffness properties on the tower bending modes may be taken into account. The model takes account of motion of the foundation mass and inertia against both translational and rotational stiffnesses. The mass and inertia of the nacelle and rotor For calculation of the tower modes, the nacelle and rotor are modelled as lumped mass and inertia located at the nacelle centre of gravity and rotor hub respectively. For one and twobladed rotors, the influence of the rotor inertia on the tower modal characteristics depends on the rotor azimuth and this may therefore be defined by the user. The variation of the tower modal frequencies with rotor azimuth is normally small and the assumption of a single rotor. 15 of 82.

(22) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. azimuthal position for the modal analysis is therefore a reasonable approximation. The user can, of course, determine the extent of the azimuthal variation in the tower modal frequencies by undertaking the modal analysis at a series of different rotor azimuths. The frequencies and mode shapes of the tower modes are computed from the eigen-values and eigen-vectors of a finite element representation of the tower structure. The finite element model of the tower is based on the use of two-dimensional beam elements to describe the mass and stiffness properties of the tower. The outputs from the modal analysis of the tower are the modal frequencies and mode shapes defined in the fore-aft and side-side directions. The modal damping coefficients are an input defined by the user and may be used to represent structural damping.. 3.2 Equations of motion Because of the complexity of the coupling of the modal degrees of freedom of the rotating and non-rotating components, the algebraic manipulation involved in the derivation of the equations of motion for a wind turbine is a complicated problem. In the case of the dynamic model within Bladed, the derivation has been carried out using energy principles and Lagrange equations by means of a computer algebra package. 3.2.1 Degrees of freedom The degrees of freedom involved in the equations of motion for the structural dynamic model for Bladed are as follows: • • • • •. Rotor out of plane including teeter, maximum six modes Rotor in-plane, maximum six modes Nacelle yaw Tower fore-aft, maximum three modes Tower side-side, maximum three modes. In addition, a sophisticated representation of the power train dynamics is offered as described in Section 4 of this manual. 3.2.2 Formulation of equations of motion The equation of motion for a single modal degree of freedom, assuming no coupling with other degrees of freedom, is as follows:. q&&i + 2. i. q& +. i i. 2 i. q = Fi / Mi. where: qi is the time dependent modal displacement,. Mi =. m(r ). 2 i. (r )dr is the modal mass,. rotor. 16 of 82.

(23) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. and:. Fi =. f (r ) i (r )dr is the modal force. rotor. Here f(r) is the distributed force over the rotor or tower component. The modal degrees of freedom are, of course, coupled and the formulation of the equations of motion within Bladed is as follows: && + [ C]q& + [ K ]q = F [ M ]q. where [M], [C] and [K] are the modal mass, damping and stiffness matrices, q is the vector of modal displacements and F the vector of modal forces. The system matrices are full due to the coupling of the degrees of freedom and contain periodic coefficients because of the time dependent interaction of the dynamics of the rotor and tower. Because of their complexity, the equations of motion are not presented in this manual. The following key comments are, however, provided: • Although the equations of motion are based on a linear modal treatment of the structural dynamics, the model does contain non-linear terms associated primarily with gyroscopic coupling. • The rotor teeter degree of freedom is provided through the first out-of-plane mode and the equation of motion includes representation of mechanical damping, stiffness and pre-load restraints as specified by the user. • The equation of motion for the nacelle yaw degree of freedom is based on the inertia of the wind turbine about the yaw axis with mechanical restraints provided through yaw damping and stiffness as specified by the user. • The aeroelasticity of the wind turbine is taken into account in the equations of motion by consideration of the interaction of the total structural velocity vector with the wind velocity vector at each element along the rotor blades. The total structural velocity vector at each element on the rotor blades is composed of the appropriate summation of the velocities associated with each structural degree of freedom. In addition to the feedback of the structural velocities into the rotor blade aerodynamics, the structural displacement associated with the rotor teeter and nacelle yaw is also taken into account. 3.2.3 Solution of the equations of motion The equations of motion are solved by time-marching integration of the differential equations using a variable step size, fourth order Runge Kutta integrator.. 17 of 82.

(24) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 3.3 Calculation of structural loads The structural loads acting on the rotor, power train and tower are computed by the appropriate summation of the applied aerodynamic loads and the inertial loads. The inertial loads are calculated by integration of the mass properties and the total acceleration vector at each station. The total acceleration vector includes modal, centrifugal, Coriolis and gravitational components.. 18 of 82.

(25) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 4. POWER TRAIN DYNAMICS The power train dynamics define the rotational degrees of freedom associated with the drive train, including drive train mountings, and the dynamics of the electrical generator. The drive train consists of a low speed shaft, gearbox and high speed shaft. Direct drive generators can also be modelled.. 4.1 Drive train models 4.1.1 Locked speed model The simplest drive train model which is available is the locked speed model, which allows no degrees of freedom for the power train. The rotor is therefore assumed to rotate at an absolutely constant speed, and the aerodynamic torque is assumed to be exactly balanced by the generator reaction torque at every instant. Clearly this model is unsuitable for start-up and shut-down simulations, but it is useful for quick, preliminary calculations of loads and performance before the drive train and generator have been fully characterised. 4.1.2 Rigid shaft model The rigid shaft model is obtained by selecting the dynamic drive train model with no shaft torsional flexibility. It allows a single rotational degree of freedom for the rotor and generator. It can be used for all calculations and is recommended if the torsional stiffness of the drive train is high. The acceleration of the generator and rotor are calculated from the torque imbalance divided by the combined inertia of the rotor and generator, making allowance for the gearbox ratio. Direct drive generators are modelled simply by setting the gearbox ratio to 1. The torque imbalance is essentially the difference between the aerodynamic torque and the generator reaction torque and any applied brake torque, taking the gearbox ratio into account. However, this is corrected to account for the inertial effect of blade deflection due to any edgewise blade vibration modes. To use the rigid shaft model, a model of the generator must also be provided, so that the generator reaction torque is defined. During a parked simulation, or once the brake has brought the rotor to rest during a stopping simulation, the actual brake torque balances the aerodynamic torque exactly (making allowance for the gearbox ratio if the brake is on the high speed shaft) and there is no further rotation. However, if the aerodynamic torque increases to overcome the maximum or applied brake torque, the brake starts to slip and rotation recommences. The rigid drive train model may be used in combination with flexible drive train mountings. In this case the equations of motion are more complex - see Section 4.3. 4.1.3 Flexible shaft model The flexible shaft model is obtained by selecting the dynamic drive train model with torsional flexibility in one or both shafts. It allows separate degrees of freedom for the rotation of the turbine rotor and the generator rotor. The torsional flexibility of the low speed and high speed shafts may be specified independently. As with the rigid shaft model, a model of the generator must be provided so that the generator reaction torque is specified.. 19 of 82.

(26) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. The turbine rotor is accelerated by the torque imbalance between the aerodynamic torque (adjusted for the effect of edgewise modes as explained in Section 4.1.2) and the low speed shaft torque. The generator rotor is accelerated by the imbalance between high speed shaft torque and generator reaction torque. The shaft torques are calculated from the shaft twist, together with any applied brake torque contributions depending on the location of the brake, which may be specified as being at either end of either the low or high speed shaft. During a parked simulation, or once the brake disk has come to rest during a stopping simulation, the equations of motion change depending on the brake location. If the brake is immediately adjacent to the rotor or generator then there is no further rotation of that component, but the other component continues to move and oscillates against the torsional flexibility of the shafts. If the brake is adjacent to the gearbox and both shafts are flexible, then both rotor and generator will oscillate. However, if the torque at the brake disk increases to overcome the maximum or applied brake torque, then the brake starts to slip again. The flexible drive train model may be used in combination with flexible drive train mountings. In this case the equations of motion are more complex - see Section 4.3. It should be pointed out that while the flexible shaft model provides greater accuracy in the prediction of loads, there is potential for one of the drive drain vibrational modes to be of relatively high frequency, depending on the generator inertia and shaft stiffnesses. The presence of this high frequency mode could result in slower simulations.. 4.2 Generator models The generator characteristics must be provided if either the rigid or flexible shaft drive train model is specified. Three generator models are available: • A directly-connected induction generator model (for constant speed turbines), • A variable speed generator model (for variable speed turbines), and • A variable slip generator model (providing limited range variable speed above rated) 4.2.1 Fixed speed induction generator This model represents an induction generator directly connected to the grid. Its characteristics are defined by the slip slope h and the short-circuit transient time constant . The air-gap or generator reaction torque Q is then defined by the following differential equation:. Q& = 1 [h( where. 0. ) Q]. is the actual generator speed and. 0. is the generator synchronous or no-load speed.. The slip slope is calculated as. Pr. h= r. (. r. 0. ). 20 of 82.

(27) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. where r is the generator speed at rated power output Pr , given by r = S is the rated slip in %, and is the full load efficiency of the generator.. 0. FINAL. (1 + S/100) where. 4.2.2 Fixed speed induction generator: electrical model A more complete model of the directly-connected induction generator is also available in Bladed. This model requires the equivalent circuit parameters of the generator to be supplied (at the operating temperature, rather than the ‘cold’ values), along with the number of pole pairs, the voltage and the network frequency. It is also possible to model power factor correction capacitors and auxiliary loads such as turbine ancillary equipment. The equivalent circuit configuration is shown in Figure 4.1. Rr/s. Rs xs. xr. xm. Ra C Xa. Rs = Stator resistance xs = Stator reactance Rr = Rotor resistance xr = Rotor reactance xm = Mutual reactance C = Power factor correction Ra = Auxiliary load resistance Xa = Auxiliary load reactance s = slip. Figure 4.1: Equivalent circuit model of induction generator The equivalent circuit parameters should be given for a star-connected generator. If the generator is delta-connected, the resistances and reactances should be divided by 3 to convert to the equivalent star-connected configuration. The voltage should be given as rms line volts. To convert peak voltage to rms, divide by 2. To convert phase volts to line volts, multiply by 3. Since this model necessarily includes electrical losses in the generator and ancillary equipment, it is not possible to specify any additional electrical losses, although mechanical losses may be specified - see Section 4.4. Four different models of the electrical dynamics of the system illustrated in Figure 4.1 are provided: • • • •. Steady state 1st order 2nd order 4th order. The steady state model simply calculates the steady-state currents and voltages in Figure 4.1 at each instant. The 1st order model introduces a first order lag into the relationship between the slip (s) and the effective rotor resistance (Rr/s), using the short-circuit transient time constant given by [4.1]:. =. X s X r x 2m XsR r s. where Xs = xs+xm, Xr = xr+xm, and. s. is the grid frequency in rad/s.. 21 of 82.

(28) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. The 2nd order model represents the generator as a voltage source reactance X’ = Xs - xm2/Xr, ignoring stator flux transients:. FINAL. behind a transient. is (rs + jX’) = vs where is and vs are the stator current and terminal voltage respectively. The dynamics of the rotor flux linkage r may be written as. 1 & r = rr i r + js ( + s ) 1 s. r. where s is the fractional slip speed (positive for generating) and ir is the rotor current. This can be re-written in terms of the induced voltage using xm r = j Xr to give. T0 & =. rs + jX s rs + jX. js. s. T0. +j. Xs X vs rs + jX. where T0 =. Xr . s rr. The 4th order model is a full d-q (direct and quadrature) axis representation of the generator which uses Park’s transformation [4.2] to model the 3-phase windings of the generator as an equivalent set of two windings in quadrature [4.3]. Using complex notation to represent the direct and quadrature components of currents and voltages as the real and imaginary parts of a single complex quantity, we can obtain. xsx r s. x 2m d i s dt i r. =. x r rs + jx 2m (1 + s) x m rs. jx m x s (1 + s). x m rr + jx m xr (1 + s) x s rr. jx s x r (1 + s). is ir. +. xr v xm s. where all the currents and voltages are now complex. Where speed of simulation is more important than accuracy, one of the lower order models should be used. The 4th order model should be used for the greatest accuracy, although in many circumstances the lower order models give very similar results. The lower order models do not give an accurate representation of start-up transients, however. 4.2.3 Variable speed generator This model should be used for a variable speed turbine incorporating a frequency converter to decouple the generator speed from the grid frequency. The variable speed drive, consisting of both the generator and frequency converter, is modelled as a whole. A modern variable speed drive is capable of accepting a torque demand and responding to this within a very short time to give the desired torque at the generator air-gap, irrespective of the generator speed (as long as it is within specified limits). A first order lag model is provided for this response:. 22 of 82.

(29) Garrad Hassan and Partners Ltd. Qg =. Document: 282/BR/009. ISSUE:011. FINAL. Qd (1 + e s). where Qd is the demanded torque, Qg is the air-gap torque, and e is the time constant of the first order lag. Note that the use of a small time constant may result in slower simulations. If the time constant is very small, specifying a zero time constant will speed up the simulations, without much effect on accuracy. A variable speed turbine requires a controller to generate an appropriate torque demand, such that the turbine speed is regulated appropriately. Details of the control models which are available with Bladed can be found in Section 5. The minimum and maximum generator torque must be specified. Motoring may occur if a negative minimum torque is specified. The phase angle between current and voltage, and hence the power factor, is specified, on the assumption that, in effect, both active and reactive power flows into the network are being controlled with the same time constant as the torque, and that the frequency converter controller is programmed to maintain constant power factor. An option for drive train damping feedback is provided. This represents additional functionality which may be available in the frequency converter controller which adds a term derived from measured generator speed onto the incoming torque demand. This term is defined as a transfer function acting on the measured speed. The transfer function is supplied as a ratio of polynomials in the Laplace operator, s. Thus the equation for the air-gap torque Qg becomes. Qg =. Qd Num(s) + (1 + e s) Den(s). g. where Num(s) and Den(s) are polynomials. The transfer function would normally be some kind of tuned bandpass filter designed to provide some damping for drive train torsional vibrations, which in the case of variable speed operation may otherwise be very lightly damped, sometimes causing severe gearbox loads. 4.2.4 Variable slip generator A variable slip generator is essentially an induction generator with a variable resistance in series with the rotor circuit [4.3, 4.4]. Below rated power, it acts just like a fixed speed induction generator, so the same parameters are required as described in Section 4.2.1. Above rated, the variable slip generator uses a fast-switching controller to regulate the rotor current, and hence the air-gap torque, so the generator actually behaves just like a variable speed system, albeit with a limited speed range. The same parameters as for a variable speed system must therefore also be supplied (see Section 4.2.3), with the exception of the phase angle since power factor control is not available in this case. Alternatively, a full electrical model of the variable slip generator is available. The generator is modelled as in Section 4.2.2, and the rotor current controller is modelled as a continuoustime PI controller which adjusts the rotor resistance between the defined limits (with. 23 of 82.

(30) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. integrator desaturation on the limits), in response to the difference between the actual and demanded rotor current. The steady-state relationship between torque and rotor current is computed at the start of the simulation, so that the torque demand can be converted to a rotor current demand. The scheme is shown in Figure 4.2. Torque demand. Current demand. 1 |I|. PI with limits. Rotor resistanc e. Measured current |I| Figure 4.2: Variable slip generator – rotor current controller. 4.3 Drive train mounting If desired, torsional flexibility may be specified either in the gearbox mounting or between the pallet or bedplate and the tower top. This option is only allowed if either the stiff or flexible drive train model is specified, and it adds an additional rotational degree of freedom. In either case, the torsional stiffness and damping of the mounting is specified, with the axis of rotation assumed to coincide with the rotor shaft. The moment of inertia of the moving components about the low speed shaft axis must also be specified. In the case of a flexible gearbox mounting, this is the moment of inertia of the gearbox casing. In the case of a flexible pallet mounting, it is the moment of inertia of the gearbox casing, the generator stator, the moving pallet and any other components rigidly fixed to it. If either form of mounting is specified, the direction of rotation of the generator shaft will affect some of the internal drive train loads. If the low speed and high speed shafts rotate in opposite directions, specify a negative gearbox ratio in the drive train model. The effect of any offset between the low speed shaft and high speed shaft axes is ignored. Any shaft brake is assumed to be rigidly mounted on the pallet. Thus any motion once the brake disk has stopped turning depends on the type of drive train mounting as well as on the position of the brake on the low or high speed shaft. For example if there is a soft pallet mounting, then there will still be some oscillation of the rotor after the brake disk has stopped even if both shafts are stiff. As in the case of the flexible shaft drive train model, it should be pointed out that while modelling the effect of flexible mountings provides greater accuracy in the prediction of loads, there is potential for one or two of the resulting drive train vibrational modes to be of relatively high frequency, depending on the various moments of inertia and shaft and mounting stiffnesses. The presence of high frequency modes could result in slower simulations.. 4.4 Energy losses Power train energy losses are modelled as a combination of mechanical losses and electrical losses in the generator (including the frequency converter in the case of variable speed turbines).. 24 of 82.

(31) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. Mechanical losses in the gearbox and/or shaft bearings are modelled as either a loss torque or a power loss, which may be constant, or interpolated linearly from a look-up table. This may be a look-up table against rotor speed, gearbox torque or shaft power, or a two-dimensional look-up table against rotor speed and either shaft torque or power. Mechanical losses modelled in terms of power are inappropriate if calculations are to be carried out at low or zero rotational speeds, e.g. for starts, stops, idling and parked calculations. In these cases, the losses are better expressed in terms of torque. The electrical losses may specified by one of two methods: Linear model: This requires a no-load loss LN and an efficiency , where the electrical power output Pe is related to the generator shaft input power Ps by: Pe =. (Ps - LN). Look-up table: The power loss L(Ps) is specified as a function of generator shaft input power Ps by means of a look-up table. The electrical power output Pe is given by: Pe = Ps - L(Ps) Linear interpolation is used between points on the look-up table. Note that if a full electrical model of the generator is used, additional electrical losses in this form cannot be specified since the generator model implicitly includes all electrical losses.. 4.5 The electrical network Provided either the detailed electrical model of the induction generator or the variable speed generator model is used, so that electrical currents and voltages are calculated, and reactive power as well as active power, then the characteristics of the network to which the turbine is connected may also be supplied. As well as allowing the voltage variations, and hence the flicker, at various points on the network to be calculated, the presence of the network may also, in the case of the directly connected induction generator, influence the dynamic response of the generator itself particularly on a weak network. The network is modelled as a connection, with defined impedance, to the point of common coupling (PCC in Figure 4.2) and a further connection, also with defined impedance, to an infinite busbar. Further turbines may be connected at the point of common coupling. These additional turbines are each assumed to be identical to the turbine being modelled, including the impedance of the connection to the point of common coupling. However they are modelled as static rather dynamic, with current and phase angle constant during the simulation. The initial conditions are calculated with the assumption that all turbines are in an identical state, and the ‘other’ turbines then remain in the same state throughout. Thus the steady state voltage rise due to all the turbines at the point of common coupling will be taken into account in calculating the performance of the turbine whose performance is being simulated .. 25 of 82.

(32) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. Other turbines (if required) Wind turbine. R1 + jX1 Windfarm interconnection impedance. PCC. Figure 4.2: The network model. 26 of 82. R2 + jX2 Network connection impedance. Infinite busbar.

(33) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. 5. CLOSED LOOP CONTROL. 5.1 Introduction Closed loop control may be used during normal running of the turbine to control the blade pitch angle and, for variable speed turbines, the rotor speed. Four different controller types are provided: 1. Fixed speed stall regulated. The generator is directly connected to a constant frequency grid, and there is no active aerodynamic control during normal power production. 2. Fixed speed pitch regulated. The generator is directly connected to a constant frequency grid, and pitch control is used to regulate power in high winds. 3. Variable speed stall regulated. A frequency converter decouples the generator from the grid, allowing the rotor speed to be varied by controlling the generator reaction torque. In high winds, this speed control capability is used to slow the rotor down until aerodynamic stall limits the power to the desired level. 4. Variable speed pitch regulated. A frequency converter decouples the generator from the grid, allowing the rotor speed to be varied by controlling the generator reaction torque. In high winds, the torque is held at the rated level and pitch control is used to regulate the rotor speed and hence also the power. For a constant speed stall regulated turbine no parameters need be defined as there is no control action. In the other cases the control action will determine the steady state operating point of the turbine as well as its dynamic response. For steady state calculations it is only necessary to specify those parameters which define the operating curve of the turbine. For dynamic calculations, further parameters are used to define the dynamics of the closed loop control. The parameters required are defined further in the following sections. Note that all closed loop control data are defined relative to the high speed shaft.. 5.2 The fixed speed pitch regulated controller This controller is applicable to a turbine with a directly-connected generator which uses blade pitch control to regulate power in high winds. It is applicable to full or partial span pitch control, as well as to other forms of aerodynamic control such as flaps or ailerons. In the latter case, the pitch angle can be taken to refer to the deployment angle of the flap or aileron. From the optimum position, the blades may pitch in either direction to reduce the aerodynamic torque. If feathering pitch action is selected, the pitchable part of the blade moves to reduce its angle of attack as the wind speed (and hence the power) increases. If stalling pitch action is selected, it moves in the opposite direction to stall the blade as the wind speed increases. In the feathering case, the minimum pitch angle defines the pitch setting below rated, while in the stalling case the maximum pitch angle is used below rated, and the pitch decreases towards the minimum value (usually a negative pitch angle) above rated.. 27 of 82.

(34) Garrad Hassan and Partners Ltd. Wind. Document: 282/BR/009. Electric power. Turbine. Blade pitch. ISSUE:011. FINAL. Power Measured transducer power Controlle. Pitch actuator. Pitch demand. Power set-point. Figure 5.1: The fixed speed pitch regulated control loop. Figure 5.1 shows schematically the elements of the fixed speed pitch regulated control loop which are modelled. 5.2.1 Steady state parameters In order to define the steady-state operating curve, it is necessary to define the power setpoint and the minimum and maximum pitch angle settings, as well as the direction of pitching as described above. The correct pitch angle can then be calculated in order to achieve the setpoint power at any given steady wind speed. 5.2.2 Dynamic parameters To calculate the dynamic behaviour of the control loop, it is necessary to specify the dynamic response of the power transducer and the pitch actuator, as well as the actual algorithm used by the controller to calculate a pitch demand in response to the measured power signal. Section 5.5 describes the available transducer and actuator models, while Section 5.6 describes the PI algorithm which is used by the controller.. 5.3 The variable speed stall regulated controller This controller model is appropriate to variable speed turbines which employ a frequency converter to decouple the generator speed from the fixed frequency of the grid, and which do not use pitch control to limit the power above rated wind speed. Instead, the generator reaction torque is controlled so as to slow the rotor down into stall in high wind speeds. The control loop is shown schematically in Figure 5.2. 5.3.1 Steady state parameters The steady-state operating curve can be described with reference to a torque-speed graph as in Figure 5.3. The allowable speed range in the steady state is from S1 to S2. In low winds it is possible to maximise energy capture by following a constant tip speed ratio load line which corresponds to operation at the maximum power coefficient. This load line is a quadratic curve on the torque-speed plane, shown by the line BG in Figure 5.3. Alternatively a look-up table may be specified. If there is a minimum allowed operating speed S1, then it is no longer possible to follow this curve in very low winds, and the turbine is then operated at nominally constant speed along the line AB shown in the figure. Similarly in high wind speeds, once the maximum operating speed S4 is reached, then once again it is necessary to 28 of 82.

(35) Garrad Hassan and Partners Ltd. Wind. Document: 282/BR/009. ISSUE:011. Generator speed. Speed transducer. Electrical power. Power Measured Controlle transducer power. FINAL. Measured speed. Turbine. Generator torque demand. Desired power, torque, speed. Figure 5.2: The variable speed stall regulated control loop depart from the optimum load line by operating at nominally constant speed along the line GH. Once maximum power is reached at point H, it is necessary to slow the rotor speed down into stall, along the constant power line HI. If high rotational speeds are allowed, it is of course possible for the line GH to collapse so that the constant power line and the constant tip speed. Figure 5.3: Variable speed stall regulated operating curve. 29 of 82.

(36) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. ratio line meet at point J. Clearly the parameters needed to specify the steady state operating curve are: • The minimum speed, S1 • The maximum speed in constant tip speed ratio mode, S4 • The maximum steady-state operating speed. This is usually S4, but could conceivably be higher in the case of a turbine whose characteristics are such that as the wind speed increases, the above rated operating point moves from H to I, then drops back to H, and then carries on (towards J) in very high winds. This situation is somewhat unlikely however, because if rotational speeds beyond S4 are permitted in very high winds, there is little reason not to increase S4 and allow the same high rotor speeds in lower winds.) • The above rated power set-point, corresponding to the line HI. This is defined in terms of shaft power. Electrical power will of course be lower if electrical losses are modelled. • The parameter K which defines the constant tip speed ratio line BG. This is given by: K =. R5 Cp( ) / 2. 3. G3. where = air density R = rotor radius = desired tip speed ratio Cp( ) = Power coefficient at tip speed ratio G = gearbox ratio Then when the generator torque demand is set to K 2 where is the measured generator speed, this ensures that in the steady state the turbine will maintain tip speed ratio and the corresponding power coefficient Cp( ). Note that power train losses may vary with rotational speed, in which case the optimum rotor speed is not necessarily that which results in the maximum aerodynamic power coefficient. As an alternative to the parameter K , a look-up table may be specified giving generator torque as a function of speed. 5.3.2 Dynamic parameters To calculate the dynamic behaviour of the control loop, it is necessary to specify the dynamic response of both power and speed transducers, as well as the actual algorithm used by the controller to calculate a generator torque demand in response to the measured power and speed signals. Section 5.5 describes the available transducer and actuator models. Two closed loop control loops are used for the generator torque control, as shown in Figure 5.4. An inner control loop calculates a generator torque demand as a function of generator speed error, while an outer loop calculates a generator speed demand as a function of power error. Both control loops use PI controllers, as described in Section 5.6. Below rated, the speed set-point switches between S1 and S4. In low winds it is at S1, and the torque demand output is limited to a maximum value given by the optimal tip speed ratio curve BG. This causes the operating point to track the trajectory ABG. In higher winds, the set-point changes to S4, and the torque demand output is limited to a minimum value given by the optimal tip speed ratio curve, causing the operating point to track the trajectory BGH. Once the torque reaches QR, the outer control loop causes the speed set-point to reduce along HI, and the inner loop tracks this varying speed demand. 30 of 82.

(37) Garrad Hassan and Partners Ltd. Document: 282/BR/009. PI controller. Power set-point. ISSUE:011. FINAL. PI controller. Speed demand. Measured power Measured speed Generator torque demand Figure 5.4: Stall regulated variable speed control loops. 5.4 The variable speed pitch regulated controller This controller model is appropriate to variable speed turbines, which employ a frequency converter to decouple the generator speed from the fixed frequency of the grid, and which use pitch control to limit the power above rated wind speed. The control loop is shown schematically in Figure 5.5. 5.4.1 Steady state parameters The steady-state operating curve can be described with reference to the torque-speed graph shown in Figure 5.6. Below rated, i.e. from point A to point H, the operating curve is exactly as in the stall regulated variable speed case described in Section 5.3.1, Figure 5.3. Above rated however, the blade pitch is adjusted to maintain the chosen operating point, designated. Wind. Generator speed. Speed transducer. Measured speed. Turbine Controlle Blade pitch. Pitch actuator. Pitch demand. Generator torque demand. Desired torque and speed. Figure 5.5: The variable speed pitch regulated control loop L. Effectively, changing the pitch alters the lines of constant wind speed, forcing them to pass through the desired operating point.. 31 of 82.

(38) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. Figure 5.6: Variable speed pitch regulated operating curve. Once rated torque is reached at point H, the torque demand is kept constant for all higher wind speeds, and pitch control regulates the rotor speed. A small (optional) margin is allowed between points H (where the torque reaches maximum) and L (where pitch control begins) to prevent excessive mode switching between below and above rated control modes. However, this margin may not be required, in which case points H and L coincide. As with the stall regulated controller, the line GH may collapse to a point if desired. Clearly the parameters needed to specify the steady state operating curve are: • The minimum speed, S1 • The maximum speed in constant tip speed ratio mode, S4 • The speed set-point above rated (S5). This may be the same as S4. • The maximum steady-state operating speed. This is normally the same as S5. • The above rated torque set-point, QR. • The parameter K which defines the constant tip speed ratio line BG, or a look-up table. This is as defined in Section 5.3.1. 5.4.2 Dynamic parameters To calculate the dynamic behaviour of the control loop, it is necessary to specify the dynamic response of the speed transducer and the pitch actuator, as well as the actual algorithm used by the controller to calculate the pitch and generator torque demands in response to the measured speed signal. Section 5.5 describes the available transducer and actuator models.. 32 of 82.

(39) Garrad Hassan and Partners Ltd. Document: 282/BR/009. ISSUE:011. FINAL. Figure 5.7 shows the control loops used to generate pitch and torque demands. The torque demand loop is active below rated, and the pitch demand loop above rated. Section 5.6 describes the PI algorithm which is used by both loops. Below rated, the speed set-point switches between S1 and S4. In low winds it is at S1, and the torque demand output is limited to a maximum value given by the optimal tip speed ratio curve BG. This causes the operating point to track the trajectory ABG. In higher winds, the set-point changes to S4, and the torque demand output is limited to a minimum value given by the optimal tip speed ratio curve, causing the operating point to track the trajectory BGH, and a maximum value of QR. When point H is reached the torque remains constant, with the pitch control loop becoming active when the speed exceeds S5. Above rated Speed set-point Below rated. Measured speed Blade. PI controller. PI controller. pitch. Generator torque demand Figure 5.7: Pitch regulated variable speed control loops. 5.5 Transducer models First order lag models are provided in Bladed to represent the dynamics of the power transducer and the generator speed transducer. The first order lag model is represented by y& =. 1 (x T. y). where x is the input and y is the output. The input is the actual power or speed and the output is the measured power or speed, as input to the controller.. 5.6 Modelling the pitch actuator The pitch actuator may be modelled as either a pitch position or pitch rate actuator, and either active or passive dynamics may be specified. The simplest model is a passive actuator, with the relationship between the input and the output represented by a transfer function. For the pitch position actuator, the input is the pitch demand generated by the controller and the output is the actual pitch angle of the blades. For the pitch rate actuator, the input is the pitch rate demand generated by the controller and the output is the actual pitch rate at which the blades move. The transfer. 33 of 82.

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